What is the integral of (3x+7)(-5x-8) ?

The integral of (3x+7)(-5x-8) is -5x^3-(59x^2)/2-56x+C

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integral of (3x+7)(-5x-8)

\int (3 x + 7) (- 5 x - 8) d x

- 5 x^{3} - \frac{59 x ^{2}}{2} - 56 x + C

Solution steps

\int (3 x + 7) (- 5 x - 8) d x

Expand

(3 x + 7) (- 5 x - 8) : - 15 x^{2} - 59 x - 56

= \int - 15 x^{2} - 59 x - 56 d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= - \int 15 x^{2} d x - \int 59 x d x - \int 56 d x

\int 15 x^{2} d x = 5 x^{3}

\int 59 x d x = \frac{59 x ^{2}}{2}

\int 56 d x = 56 x

= - 5 x^{3} - \frac{59 x ^{2}}{2} - 56 x

Add a constant to the solution

= - 5 x^{3} - \frac{59 x ^{2}}{2} - 56 x + C

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What is the integral of (3x+7)(-5x-8) ?
The integral of (3x+7)(-5x-8) is -5x^3-(59x^2)/2-56x+C